Combining state estimator and disturbance observer in discrete‐time sliding mode controller design

In response to a multiple input/multiple output discrete‐time linear system with mismatched disturbances, an algorithm capable of performing estimated system states and unknown disturbances is proposed first, and then followed with the design of the controller. Attributed to the fact that both system states and disturbances can be estimated simultaneously with our proposed method, the estimation error is constrained at less than O(T) as the disturbance between the two sampling points is insignificant. In addition, the estimated system states and disturbances are then to be used in the controller when implementing our algorithm in a non‐minimum phase system (with respect to the relation between the output and the disturbance). The tracking error is constrained in a small bounded region and the system stability is guaranteed. Finally, a numerical example is presented to demonstrate the applicability of the proposed control scheme. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Sliding Mode Observer based Fault Estimation for Certain Class of Uncertain Nonlinear Systems

This paper proposes a new scheme for estimating the actuator and sensor fault for Lipschitz nonlinear systems with unstructured uncertainties using the sliding mode observer (SMO) technique. Initially, a coordinate transformation is introduced to transform the original state vector into two parts such that the actuator faults only appear in the dynamics of the second state vector. The concept of equivalent output error injection is then employed to estimate the actuator fault. The effects of system uncertainties on the estimation errors of states and faults are minimized by integrating an uncertainty attenuation level into the observer. The sufficient conditions for the state estimation error to be bounded and satisfy a prescribed performance are derived and expressed as a linear matrix inequality (LMI) optimization problem. Furthermore, the proposed actuator fault estimation method is extended to sensor fault estimation. Finally, the effectiveness of the proposed scheme in estimating actuator and sensor faults has been illustrated considering an example of a single‐link flexible joint robot system.     

一种新型三阶固定时间收敛滑模非线性扩张状态观测器

为了解决传统扩张状态观测器存在对系统状态跟踪速度慢、跟踪精度低的问题,基于滑模控制方法设计一种新型三阶固定时间收敛滑模非线性扩张状态观测器,并对其收敛时间和稳态误差进行分析.首先,提出一种新型固定时间收敛滑模面和滑模趋近律,并借助滑模控制方法设计得到滑模非线性扩张状态观测器;然后,利用Lyapunov函数证明该滑模非线性扩张状态观测器能够实现固定时间收敛,并分析其对系统扰动的估计误差;最后,仿真对比实验表明,与传统扩张状态观测器相比,所提出滑模非线性扩张状态观测器能够实现对系统状态快速且高精度的跟踪、具有显著的性能优势.     

Robust Nonlinear Observer And Observer‐Backstepping Control Design For Surface Ships

A robust passive non‐linear observer, utilizing the sliding mode concept and acceleration feedback (AFB) technique, is developed for ships. The main advantage of the proposed observer is that it is robust and that it takes the Coriolis‐centripetal matrix (C‐matrix) into account. The observer reconstructs velocities of ships and bias from slowly varying environmental disturbances. It also filters out the noise and wave frequency data from measurements to protect the actuators from wear and excessive fuel consumption. The sliding mode technique is introduced to improve robust performance against neglected disturbances, uncertainties, and unmodeled dynamics. The acceleration feedback technique and coordinate transformation are used for reshaping the inertia matrix and removing the C‐matrix from the mathematical model. Then, the observer design and stability analysis become simpler. An output feedback controller using observer backstepping and the Lyapunov redesign technique is derived, and the global stability of the observer and observer‐controller system is shown by Lyapunov stability theory. A set of simulations was carried out to verify the performance of the proposed observer and controller.     

一类非线性系统的自适应时延观测器设计(英文)

利用输出差分及滑模方法研究一类非线性系统的自适应时延状态观测器设计问题. 首先将系统输出的微分及高阶微分用输出和其延迟测量值的差商来表示, 然后在此基础上构造了一种时延状态观测器, 估计误差的影响可由滑模项来消除. 在系统满足线性参数化的条件下给出了一种自适应时延状态观测器设计. 最后给出仿真研究说明设计方法的有效性.